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Traditional integrating spheres, which use a single detector to measure luminous flux, have a number of drawbacks associated with the sources of error caused by baffling, nonideal topology, and variations in surface reflectance. In this article we address the potential drawbacks of many traditional integrating spheres and present a new instrument which achieves accurate measurements without the use of baffles, by relying on optical fibers to distribute measurement points around the interior of a highly reflective structure.